Abstract:
In the paper we study the reproducing of the initial phase of the inner turbulence (without regard for the boundary effects). The atypical regularization of multiple-component Euler system is made by the viscosity and diffuse layering introduction. The analogue of Hugoniot condition and the analogue of Lax stability condition are constructed for it. The problem of local accessibility of the phase space points is investigated. The bifurcations of one-front solutions of the abridged Euler system to the two-front solutions are obtained. The supersonic behaviour of bifurcations appearance is shown. The reconstruction of the initial phase of the inner turbulence (without regard for the boundary effects) is made including the mathematical description of the birth of two-speed flow (the Riemann–Hugoniot catastrophe) and alternation.
Citation:
N. N. Yakovlev, E. A. Lukashev, E. V. Radkevich, V. V. Palin, “On the inner turbulence paradigm”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 19:1 (2015), 155–185
This publication is cited in the following 5 articles:
E. V. Radkevich, E. A. Lukashev, O. A. Vasil'yeva, “Rayleigh-benard instability: a study by the methods of Cahn–Hillard theory of nonequilibrium phase transitions”, J. Math. Sci. (N. Y.), 244:2 (2020), 294–319
E. V. Radkevich, E. A. Lukashev, M. I. Sidorov, O. A. Vasil'eva, “Methods of nonlinear dynamics of nonequilibrium processes in fracture mechanics”, Eurasian Journal of Mathematical and Computer Applications, 6:2 (2018), 43–80
E. A. Lukashev, E. V. Radkevich, M. I. Sidorov, O. A. Vasil'eva, “Investigation of the process of destruction of structural materials by the method of mathematical reconstruction in the form of a nonequilibrium phase transition”, AIP Conference Proceedings, 2048 (2018), 020001
A. A. Andreyev, V. P. Padchenko, E. A. Kozlova, “To the 75th anniversary of professor Evgeniy Vladimirovich Radkevich”, Vestn. Samar. Gos. Tekhnicheskogo Univ.-Ser. Fiz.-Mat. Nauka, 22:1 (2018), 7–14
E. V. Radkevich, E. A. Lukashev, M. I. Sidorov, O. A. Vasil'eva, “Methods of nonlinear dynamics of nonequilibrium processes in fracture mechanics”, Eurasian J. Math. Comput. Appl., 6:2 (2018), 43–80
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